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A224145 Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing. 1

%I

%S 29,239,1037,3296,8838,21183,46586,95455,184222,337727,592178,998751,

%T 1627894,2574399,3963306,5956703,8761486,12638143,17910626,24977375,

%U 34323558,46534591,62311002,82484703,108036734,140116543,180062866

%N Number of n X 7 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.

%C Column 7 of A224146.

%H R. H. Hardin, <a href="/A224145/b224145.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (4/315)*n^7 + (4/45)*n^6 + (34/45)*n^5 + (29/9)*n^4 + (508/45)*n^3 + (1156/45)*n^2 + (1328/35)*n - 161 for n>4.

%F Conjectures from _Colin Barker_, Aug 28 2018: (Start)

%F G.f.: x*(29 + 7*x - 63*x^2 + 68*x^3 + 152*x^4 - 199*x^5 + 28*x^6 + 71*x^7 - 21*x^8 - 12*x^9 + 3*x^10 + x^11) / (1 - x)^8.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>12.

%F (End)

%e Some solutions for n=3:

%e ..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..0..0..0

%e ..0..0..1..1..1..1..0....0..0..1..0..0..0..0....0..0..0..1..1..1..0

%e ..0..0..1..1..1..1..1....0..0..1..0..0..0..0....0..0..0..1..1..1..1

%Y Cf. A224146.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 31 2013

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Last modified September 18 17:45 EDT 2019. Contains 327178 sequences. (Running on oeis4.)